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A321976 7-dimensional Catalan numbers.

%I A321976 #24 Sep 08 2022 08:46:23
%S A321976 1,1,429,1385670,13672405890,278607172289160,9490348077234178440,
%T A321976 475073684264389879228560,32103104214166146088869942000,
%U A321976 2760171874087743799855959353857200,289232890341906497299306268771988273600,35764585916110766978895474668714467232388000
%N A321976 7-dimensional Catalan numbers.
%C A321976 Number of n X 7 Young tableaux.
%H A321976 Seiichi Manyama, <a href="/A321976/b321976.txt">Table of n, a(n) for n = 0..177</a>
%H A321976 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hook_length_formula">Hook length formula</a>
%F A321976 a(n) = 0!*1!*...*6! * (7*n)! / ( n!*(n+1)!*...*(n+6)! ).
%F A321976 a(n) ~ 3110400 * 7^(7*n + 1/2) / (Pi^3 * n^24). - _Vaclav Kotesovec_, Nov 23 2018
%t A321976 Table[24883200*(7*n)!/(n!*(n+1)!*(n+2)!*(n+3)!*(n+4)!*(n+5)!*(n+6)!),{n,0,15}] (* _Vincenzo Librandi_, Nov 24 2018 *)
%o A321976 (PARI) {a(n) = 24883200*(7*n)!/(n!*(n+1)!*(n+2)!*(n+3)!*(n+4)!*(n+5)!*(n+6)!)}
%o A321976 (Magma) [24883200*Factorial(7*n) / (Factorial(n)*Factorial(n + 1)*Factorial(n + 2)*Factorial(n + 3)*Factorial(n + 4)*Factorial(n + 5)*Factorial(n + 6)): n in [0..15]]; // _Vincenzo Librandi_, Nov 24 2018
%o A321976 (GAP) List([0..15],n->24883200*Factorial(7*n)/Product([0..6],k->Factorial(n+k))); # _Muniru A Asiru_, Nov 25 2018
%Y A321976 Row 7 of A060854.
%Y A321976 Cf. A000108, A005789, A005790, A005791, A321975.
%K A321976 nonn
%O A321976 0,3
%A A321976 _Seiichi Manyama_, Nov 23 2018